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<div class="subTitle">org.apache.commons.math3.linear</div>
<h2 title="Class CholeskyDecomposition" class="title">Class CholeskyDecomposition</h2>
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<pre>public class <span class="strong">CholeskyDecomposition</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Calculates the Cholesky decomposition of a matrix.
 <p>The Cholesky decomposition of a real symmetric positive-definite
 matrix A consists of a lower triangular matrix L with same size such
 that: A = LL<sup>T</sup>. In a sense, this is the square root of A.</p>
 <p>This class is based on the class with similar name from the
 <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
 following changes:</p>
 <ul>
   <li>a <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getLT()"><code>getLT</code></a> method has been added,</li>
   <li>the <code>isspd</code> method has been removed, since the constructor of
   this class throws a <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear"><code>NonPositiveDefiniteMatrixException</code></a> when a
   matrix cannot be decomposed,</li>
   <li>a <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getDeterminant()"><code>getDeterminant</code></a> method has been added,</li>
   <li>the <code>solve</code> method has been replaced by a <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getSolver()"><code>getSolver</code></a> method and the equivalent method provided by the returned
   <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><code>DecompositionSolver</code></a>.</li>
 </ul></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>2.0 (changed to concrete class in 3.0)</dd>
<dt><span class="strong">Version:</span></dt>
  <dd>$Id: CholeskyDecomposition.java 1566017 2014-02-08 14:13:34Z tn $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>, 
<a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a></dd></dl>
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<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD">DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</a></strong></code>
<div class="block">Default threshold below which diagonal elements are considered null
 and matrix not positive definite.</div>
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<tr class="rowColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD">DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</a></strong></code>
<div class="block">Default threshold above which off-diagonal elements are considered too different
 and matrix not symmetric.</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)">CholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</code>
<div class="block">Calculates the Cholesky decomposition of the given matrix.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)">CholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                     double&nbsp;relativeSymmetryThreshold,
                     double&nbsp;absolutePositivityThreshold)</code>
<div class="block">Calculates the Cholesky decomposition of the given matrix.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getDeterminant()">getDeterminant</a></strong>()</code>
<div class="block">Return the determinant of the matrix</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getL()">getL</a></strong>()</code>
<div class="block">Returns the matrix L of the decomposition.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getLT()">getLT</a></strong>()</code>
<div class="block">Returns the transpose of the matrix L of the decomposition.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getSolver()">getSolver</a></strong>()</code>
<div class="block">Get a solver for finding the A &times; X = B solution in least square sense.</div>
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<pre>public static final&nbsp;double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</pre>
<div class="block">Default threshold above which off-diagonal elements are considered too different
 and matrix not symmetric.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.linear.CholeskyDecomposition.DEFAULT_RELATIVE_SYMMETRY_THRESHOLD">Constant Field Values</a></dd></dl>
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<pre>public static final&nbsp;double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</pre>
<div class="block">Default threshold below which diagonal elements are considered null
 and matrix not positive definite.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.linear.CholeskyDecomposition.DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD">Constant Field Values</a></dd></dl>
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<h4>CholeskyDecomposition</h4>
<pre>public&nbsp;CholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</pre>
<div class="block">Calculates the Cholesky decomposition of the given matrix.
 <p>
 Calling this constructor is equivalent to call <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)"><code>CholeskyDecomposition(RealMatrix, double, double)</code></a> with the
 thresholds set to the default values <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><code>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</code></a> and <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><code>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</code></a>
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - the matrix to decompose</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the matrix is not square.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSymmetricMatrixException.html" title="class in org.apache.commons.math3.linear">NonSymmetricMatrixException</a></code> - if the matrix is not symmetric.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if the matrix is not
 strictly positive definite.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)"><code>CholeskyDecomposition(RealMatrix, double, double)</code></a>, 
<a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><code>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</code></a>, 
<a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><code>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</code></a></dd></dl>
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<pre>public&nbsp;CholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                     double&nbsp;relativeSymmetryThreshold,
                     double&nbsp;absolutePositivityThreshold)</pre>
<div class="block">Calculates the Cholesky decomposition of the given matrix.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - the matrix to decompose</dd><dd><code>relativeSymmetryThreshold</code> - threshold above which off-diagonal
 elements are considered too different and matrix not symmetric</dd><dd><code>absolutePositivityThreshold</code> - threshold below which diagonal
 elements are considered null and matrix not positive definite</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the matrix is not square.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSymmetricMatrixException.html" title="class in org.apache.commons.math3.linear">NonSymmetricMatrixException</a></code> - if the matrix is not symmetric.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if the matrix is not
 strictly positive definite.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)"><code>CholeskyDecomposition(RealMatrix)</code></a>, 
<a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><code>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</code></a>, 
<a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><code>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</code></a></dd></dl>
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<h4>getL</h4>
<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;getL()</pre>
<div class="block">Returns the matrix L of the decomposition.
 <p>L is an lower-triangular matrix</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the L matrix</dd></dl>
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<h4>getLT</h4>
<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;getLT()</pre>
<div class="block">Returns the transpose of the matrix L of the decomposition.
 <p>L<sup>T</sup> is an upper-triangular matrix</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the transpose of the matrix L of the decomposition</dd></dl>
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<h4>getDeterminant</h4>
<pre>public&nbsp;double&nbsp;getDeterminant()</pre>
<div class="block">Return the determinant of the matrix</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>determinant of the matrix</dd></dl>
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<h4>getSolver</h4>
<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</a>&nbsp;getSolver()</pre>
<div class="block">Get a solver for finding the A &times; X = B solution in least square sense.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a solver</dd></dl>
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